Non-Archimedean Quantum Mechanics via Quantum Groups
arXiv:2210.03071 · doi:10.1016/j.nuclphysb.2022.116021
Abstract
We present a new non-Archimedean realization of the Fock representation of the q-oscillator algebras where the creation and annihilation operators act on complex-valued functions, which are defined on a non-Archimedean local field of arbitrary characteristic, for instance, the field of p-adic numbers. This new realization implies that a large number of quantum models constructed using q-oscillator algebras are non-Archimedean models, in particular, p-adic quantum models. In this framework, we select a q-deformation of the Heisenberg uncertainty relation, and construct the corresponding q-deformed Schrödinger equations. In this way we construct a p-adic quantum mechanics which is a p-deformed quantum mechanics. We also solve the time-independent Schrödinger equations for the free particle, and a particle in a non-Archimedean box. In the last case we show the existence of a discrete sequence of energy levels. We determine the eigenvalues of Schrödinger operator for a general radial potential. By choosing the potential in a suitable form we recover the energy levels of the q-hydrogen atom.
arXiv commentFinal version. To appear in Nuclear Physics B
References in corpus (15)
- p-Adic Mathematical Physics
- Wavelet analysis as a p-adic spectral analysis
- -adic AdS/CFT
- Basic-deformed thermostatistics
- Thermostatistics of deformed bosons and fermions
- Basic-deformed quantum mechanics
- A q-deformed Quantum Mechanics
- Deformed quantum mechanics and q-Hermitian operators
- Spectrum of q-Deformed Schrödinger Equation
- A q-deformed Uncertainty Relation
- Signs of the time: Melonic theories over diverse number systems
- Deformed quantum statistics in two-dimensions
- Meromorphic Continuation of Koba-Nielsen String Amplitudes
- On -adic string amplitudes in the limit approaches to one
- Quantum Groups and Field Theory